8.5: The Least Upper Bound Property
DEFINITION. Upper bound Let \(X \subset \mathcal{D}\) . We say that \(X\) is bounded above if there is \(M \in \mathcal{D}\) such that \[(\forall x \in X) x \leq M .\] In this event we say that \(M\) is an upper bound for \(X\) .
DEFINITION. Least upper bound Let \(X \subset \mathcal{D}\) be bounded above. Suppose \(M\) is an upper bound for \(X\) such that for any upper bound \(N\) for \(X, M \leq N\) . Then the number \(M\) is called the least upper bound for \(X\) .
Lower bound and greatest lower bound are defined analogously.
THEOREM 8.3. Least Upper Bound Property If \(X\) is a non-empty subset of \(\mathcal{D}\) and is bounded above, then \(X\) has a least upper bound. If it is bounded below, then it has a greatest lower bound.
PROOF. Let \(X \subset \mathcal{D}\) be bounded above. Let \[M=\bigcup_{L \in X} L \subseteq \mathbb{Q} .\] The set \(M\) is bounded above (why?), and hence \(M \neq \mathbb{Q}\) . Any element of \(M\) is an element of some \(L \in X\) , and consequently cannot be a maximal element of \(L\) . Therefore \(M\) has no largest element. If \(a \in M\) , \(c \in \mathbb{Q}\) and \(c<a\) then \(c \in M\) . Therefore \(M\) is a Dedekind cut. For any \(L \in X, L \subseteq M\) and hence \[L \leq M .\] That is, \(M\) is an upper bound for \(X\) .
Let \(K<M\) . Then there is \(a \in M \backslash K\) . So \(a\) is in some \(L_{0}\) in \(X\) . Therefore \(L_{0}\) is not contained in \(K\) and \(K\) is not an upper bound for \(X\) . It follows that \(M\) is the least upper bound for \(X\) .
We leave the argument for the existence of a greatest lower bound to the reader.
The least upper bound property is the essential property of real numbers that permits the main theorems of calculus. It is the reason we use this large set, rather than, say, the algebraic numbers. It uniquely characterizes the real numbers as an extension of the rational numbers - see Theorem \(8.23\) for a precise statement.
Now that we have proved this key property, we shall use \(\mathbb{R}\) to denote the set of real numbers, identifying a real number \(\alpha\) with the Dedekind cut \((-\infty, \alpha) \cap \mathbb{Q}\) . We shall no longer need to concern ourselves with Dedekind cuts per se.


13.5.1: Imprinted Genes
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Imprinted genes are genes whose expression is determined by the parent that contributed them. Imprinted genes violate the usual rule of inheritance that both alleles in a heterozygote are equally expressed.
Examples of the usual rule :
- If a child inherits the gene for blood group A from either parent and the gene for group B from the other parent, the child's blood group will be AB .
- If a child inherits the gene encoding hemoglobin A from either parent and the gene encoding hemoglobin S from the other parent, the child's red blood cells will contain roughly equal amounts of the two types of hemoglobin.
But there are a few exceptions to this rule. A small number of genes in mammals (~80 of them at a recent count) and in angiosperms have been found to be imprinted . Because most imprinted genes are repressed, either
- the maternal (inherited from the mother) allele is expressed exclusively because the paternal (inherited from the father) allele is imprinted or
- vice versa.
The process begins during gamete formation when
- in males certain genes are imprinted in developing sperm and
- in females, others are imprinted in the developing egg.
All the cells in a resulting child will have the same set of imprinted genes from both its father and its mother EXCEPT for those cells ("germplasm") that are destined to go on to make gametes. All imprints — both maternal and paternal — are erased in them.
Examples
IGF2
— the gene encoding the insulin-like growth factor-2
In humans (and other mammals like mice and pigs) the IGF2 allele inherited from the father (paternal) is expressed; the allele inherited from the mother is not.
If both alleles should begin to be expressed in a cell, that cell may develop into a cancer.
IGF2r
— the gene encoding the cell receptor for Igf-2
In mice the IGF2r allele inherited from the mother is expressed; that from the father is not. Differential imprinting accounts for this, and the mechanism is described below.
XIST
— the gene encoding the RNA that converts one of the X chromosomes in a female cell into an inactive Barr body . This process is random in the cells of the female fetus and thus is NOT an example of imprinting. However, all the cells of her extraembryonic membranes (which form the amnion, placenta, and umbilical cord) have the father's X chromosome inactivated. Imprinting of the XIST locus accounts for this.
Mechanism of parental imprinting
The process of imprinting starts in the gametes where the allele destined to be inactive in the new embryo (either the father's or the mother's as the case may be) is "marked". The mark appears to be methylation of the DNA in the promoter(s) of the gene.
Methyl groups are added to cytosines (Cs) in the DNA. When this occurs at stretches of alternating Cs and Gs called CpG sites in a promoter, it prevents binding of transcription factors to the promoter thus shutting down expression of the gene.
Although methylation seems to be the imprinting signal , keeping the gene shut down may require the production of RNA .
Methylation — and thus inactivation — of the promoters of tumor suppressor genes is frequently found in cancer cells.
The IGF2r gene
A report in
Nature
(16 October 1997) by Wutz et al, reveals that:
In the mother's (
maternal
) copy of the gene,
- there is an upstream (left) promoter that is unmethylated and active
- binding of transcription factors to this upstream promoter enables transcription of the sense strand of the gene to produce Igf2r messenger RNA .
- There is also a downstream set of CpG sites that are methylated
In the father's ( paternal ) copy of the IGF2r gene (the imprinted version)
- the promoter for IGF2r transcription is methylated (and inactive),
- but the downstream promoter is unmethylated and active.
- Transcription of the antisense strand from the downstream promoter produces an antisense RNA (a long noncoding RNA) that participates in shutting his gene down.
XIST
The XIST locus on the X chromosome encodes a long noncoding RNA that shuts down all (or almost all) of the other genes on the chromosome, converting it into an inactive Barr body .
Is imprinting important?
Yes.
- Deliberate (in mice) or accidental (in humans) inheritance of two copies of a particular chromosome from one parent and none from the other parent is usually fatal (even though a complete genome is present).
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Inheritance of two copies of one of mother's genes and no copy of the father's (or vice versa) can produce serious developmental defects.
- Failure to inherit several nonimprinted genes on the father's chromosome #15 causes a human congenital disorder called Prader-Willi syndrome .
- Absence or mutation of a nonimprinted gene ( UBE3A ) on the mother's chromosome #15 causes Angelman syndrome .
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Failure of imprinting in somatic cells may lead to
cancer
.
- The cancerous cells in some cases of a malignancy called Wilms´ tumor and many cases of colon cancer have both copies of the IGF2 gene expressed (where only one, the father's, should be).
- Reduced methylation — and hence increased expression — of proto-oncogenes can lead to cancer, while
- increased methylation — and hence decreased expression — of tumor suppressor genes can also do so.
Imprinting and Parthenogenesis
Imprinting is the reason that parthenogenesis ("virgin birth") does not occur in mammals. Two complete female genomes cannot produce viable young because of the imprinted genes. For example, the embryo needs the father's Igf2 gene because the mother's copy has been imprinted and is inactive.
- An insulator — with a bound protein designated CTCF ("CCCTC binding factor") (named for a nucleotide sequence found in all insulators) — prevents her Igf2 gene from interacting with the enhancers needed to turn it ON.
- The father's copy of the gene can be turned on because methylation of his insulator prevents binding by CTCF so the enhancers can interact with the gene.
However, two healthy laboratory mice have been produced by parthenogenesis; that is, containing two female (haploid) genomes. (See Kono, T. et al ., Nature , 22 April 2004.)
This was done by fusing two oocytes (thus each cell haploid):
- a normal oocyte with its imprinted (inactivated) Igf2 gene
-
an immature oocyte
- harvested before imprinting occurs and
- containing a deletion of the insulator that blocks enhancer activation of the Igf2 gene. Thus the Igf2 gene from this oocyte could be expressed in the developing embryo.
Out of several hundred attempts, two resulting blastocysts not only implanted successfully in a surrogate mother but went on to be born normally. One even grew up and had babies of her own.
Imprinting in Plants
Some genes in the endosperm of angiosperms are imprinted by the addition of methyl groups. For some, both maternal copies (endosperm is 3n ) are expressed (demethylated) while the male allele remains shut down. For other genes, it is the female alleles that are imprinted and thus not expressed while the male allele is functional.


12.5: Cloning DNA - Plasmid Vectors
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- Ying Liu
- City College of San Francisco
Plasmids are Naturally Present in Some Bacteria
Many bacteria contain extra-chromosomal DNA elements called plasmids . These are usually small (a few 1000 bp), circular, double stranded molecules that replicate independently of the chromosome and can be present in high copy numbers within a cell. In the wild, plasmids can be transferred between individuals during bacterial mating and are sometimes even transferred between different species. Plasmids are particularly important in medicine because they often carry genes for pathogenicity and drug-resistance. In the lab, plasmids can be inserted into bacteria in a process called transformation.
Using Plasmids as Cloning Vectors
To insert a DNA fragment into a plasmid, both the fragment and the circular plasmid are cut using a restriction enzyme that produces compatible ends (Figure \(\PageIndex{1}\)). Given the large number of restriction enzymes that are currently available, it is usually not too difficult to find an enzyme for which corresponding recognition sequences are present in both the plasmid and the DNA fragment, particularly because most plasmid vectors used in molecular biology have been engineered to contain recognition sites for a large number of restriction endonucleases.
After restriction digestion, the desired fragments may be further purified or selected before they are mixed together with ligase to join them together. Following a short incubation, the newly ligated plasmids, containing the gene of interest are transformed into E. coli . Transformation is accomplished by mixing the ligated DNA with E. coli cells that have been specially prepared (i.e. made competent ) to uptake DNA. Competent cells can be made by exposure to compounds such as CaCl 2 or to electrical fields ( electroporation ). Because only a small fraction of cells that are mixed with DNA will actually be transformed, a selectable marker , such as a gene for antibiotic resistance, is usually also present on the plasmid. After transformation (combining DNA with competent cells), bacteria are spread on a bacterial agar plate containing an appropriate antibiotic so that only those cells that have actually incorporated the plasmid will be able to grow and form colonies. This can then be picked and used for further study.
Molecular biologists use plasmids as vectors to contain, amplify, transfer, and sometimes express genes of interest that are present in the cloned DNA. Often, the first step in a molecular biology experiment is to clone (i.e. copy) a gene into a plasmid, then transform this recombinant plasmid back into bacteria so that essentially unlimited copies of the gene (and the plasmid that carries it) can be made as the bacteria reproduce. This is a practical necessity for further manipulations of the DNA, since most techniques of molecular biology are not sensitive enough to work with just a single molecule at a time. Many molecular cloning and recombination experiments are therefore iterative processes in which:
- a DNA fragment (usually isolated by PCR and/or restriction digestion) is cloned into a plasmid cut with a compatible restriction enzyme
- the recombinant plasmid is transformed into bacteria
- the bacteria are allowed to multiply, usually in liquid culture
- a large quantity of the recombinant plasmid DNA is isolated from the bacterial culture
- further manipulations (such as site directed mutagenesis or the introduction of another piece of DNA) are conducted on the recombinant plasmid
- the modified plasmid is again transformed into bacteria, prior to further manipulations, or for expression
An Application of Molecular Cloning: Production of Recombinant Insulin
Purified insulin protein is critical to the treatment of diabetes. Prior to ~1980, insulin for clinical use was isolated from human cadavers or from slaughtered animals such as pigs. Human-derived insulin generally had better pharmacological properties, but was in limited supply and carried risks of disease transmission. By cloning the human insulin gene and expressing it in E. coli , large quantities of insulin identical to the human hormone could be produced in fermenters, safely and efficiently. Production of recombinant insulin also allows specialized variants of the protein to be produced: for example, by changing a few amino acids, longer-acting forms of the hormone can be made. The active insulin hormone contains two peptide fragments of 21 and 30 amino acids, respectively. Today, essentially all insulin is produced from recombinant sources (Figure \(\PageIndex{2}\)), i.e. human genes and their derivatives expressed in bacteria or yeast.


6.3: The Nebular Theory
So…how did the solar system form and end up with all these different types of objects? Currently the best theory is the Nebular Theory . This states that the solar system developed out of an interstellar cloud of dust and gas, called a nebula . This theory best accounts for the objects we currently find in the Solar System and the distribution of these objects. The Nebular Theory would have started with a cloud of gas and dust, most likely left over from a previous supernova. The nebula started to collapse and condense; this collapsing process continued for some time. The Sun-to-be collected most of the mass in the nebula’s center, forming a Protostar .
A protostar is an object in which no nuclear fusion has occurred, unlike a star that is undergoing nuclear fusion. A protostar becomes a star when nuclear fusion begins. Most likely the next step was that the nebula flattened into a disk called the Protoplanetary Disk ; planets eventually formed from and in this disk.
Three processes occurred with the nebular collapse:
- The orderly motions of the solar system today are a direct result of the solar system’s beginnings in a spinning, flattened cloud of gas and dust.


1.11.1: Gibbs-Duhem Equation
This equation is at the heart of chemical thermodynamics. The Gibbs energy of a closed system can be expressed as follows.
\[\mathrm{G}=\mathrm{G}\left[\mathrm{T}, \mathrm{p}, \mathrm{n}_{\mathrm{i}}\right] \nonumber \]
Here \(\mathrm{n}_{\mathrm{i}}\) represents the amounts of all chemical substances in the system. Then for a system containing two chemical substances, 1 and 2,
\[\mathrm{G}=\mathrm{G}\left[\mathrm{T}, \mathrm{p}, \mathrm{n}_{1}, \mathrm{n}_{2}\right] \nonumber \]
If we prepare a system containing \(\mathrm{k} \, \mathrm{n}_{1}\) and \(\mathrm{k} \, \mathrm{n}_{2}\) moles of the two chemical substances [cf. Euler’s Theorem], the Gibbs energy increases by a factor, \(\mathrm{k}\). Hence,
\[\mathrm{G}=\mathrm{n}_{1} \, \mu_{1}+\mathrm{n}_{2} \, \mu_{2} \nonumber \]
In general [1],
\[\mathrm{G}=\sum_{\mathrm{j}=1}^{\mathrm{j}=\mathrm{i}} \mathrm{n}_{\mathrm{j}} \, \mu_{\mathrm{j}} \nonumber \]
Equation (c) is differentiated [2].
\[\mathrm{dG}=\mathrm{n}_{1} \, \mathrm{d} \mu_{1}+\mu_{1} \, \mathrm{dn} \mathrm{n}_{1}+\mathrm{n}_{2} \, \mathrm{d} \mu_{2}+\mu_{2} \, \mathrm{dn}_{2} \nonumber \]
But [3],
\[\mathrm{dG}=-\mathrm{S} \, \mathrm{dT}+\mathrm{V} \, \mathrm{dp}+\mu_{1} \, \mathrm{dn}_{1}+\mu_{2} \, \mathrm{dn}_{2} \nonumber \]
Therefore, combining equations (c) and (f),
\[-S \, d T+V \, d p-n_{1} \, d \mu_{1}-n_{2} \, d \mu_{2}=0 \nonumber \]
Therefore, for a system held at fixed \(\mathrm{T}\) and \(\mathrm{p}\) [4],
\[\mathrm{n}_{1} \, \mathrm{d} \mu_{1}+\mathrm{n}_{2} \, \mathrm{d} \mu_{2}=0 \nonumber \]
Equation (h) expresses the ‘communication’ between the two chemical substances in the system. In some senses equation (h) is a Happy Family Equation. If the chemical potential of substance 1, \(\mu_{1}\) increases [i.e. \(\mathrm{d} \mu_{1}> 0\)], the chemical potential of chemical substance 2 decreases, [i.e. \(\mathrm{d} \mu_{2}<0\)], in order to hold the condition expressed by equation (h) [5].
Footnotes
[1] Similarly \(\mathrm{U}=\sum_{\mathrm{j}=1}^{\mathrm{j}=\mathrm{i}} \mathrm{n}_{\mathrm{j}} \, \mu_{\mathrm{j}}+\mathrm{T} \, \mathrm{S}-\mathrm{p} \, \mathrm{V}\) \(\mathrm{H}=\sum_{\mathrm{j}=1}^{\mathrm{j}=\mathrm{i}} \mathrm{n}_{\mathrm{j}} \, \mu_{\mathrm{j}}+\mathrm{T} \, \mathrm{S}\) and \(F=\sum_{j=1}^{j=i} n_{j} \, \mu_{j}-p \, V\)
[2] Generally, \(\mathrm{dG}=\sum_{\mathrm{j}=1}^{\mathrm{j}=\mathrm{i}}\left[\mathrm{n}_{\mathrm{j}} \, \mathrm{d} \mu_{\mathrm{j}}+\mu_{\mathrm{j}} \, \mathrm{dn} \mathrm{n}_{\mathrm{j}}\right]\)
[3] Generally \(\mathrm{dG}=-\mathrm{S} \, \mathrm{dT}+\mathrm{V} \, \mathrm{dp}+\sum_{\mathrm{j}=1}^{\mathrm{j}=\mathrm{i}} \mu_{\mathrm{j}} \, \mathrm{dn}_{\mathrm{j}}\(
[4] Generally \(\sum_{j=1}^{j=i} n_{j} \, d \mu_{j}=0\)
[5] If one member of a family is sad for some reason, other members of the family say something along the lines, ‘cheer up --it is not as bad as all that’. If another member of the family becomes over-excited, the family says something along the lines, ‘calm down’. Similar things happen to chemical substances in a closed system at fixed \(\mathrm{T}\) and \(\mathrm{p}\).


8.4: Advantages, Disadvantages, and Considerations
What you’ll learn to do: discuss the advantages, disadvantages, and important considerations of starting a small business
As author and retired entrepreneur Carol Denbow writes in Are Your Ready to Be Your Own Boss?, “If you want your new business to succeed, you must know why most businesses fail.” New business survival statistics are grim. From 2005–2017, approximately 21% of new businesses failed in the first year. Roughly half of new business fail within 4 years. And only 33% of new businesses survive for 10 or more years. Why do you think that is? Denbow’s next sentence provides a clue: “Most people spend more time planning their vacations than they do their new businesses.” In this section, we’ll discuss the pros and cons of starting a small business and, in particular, how to improve the odds of success.
Learning Objectives
- Explain why some business ventures fail
- List important considerations in deciding to start a business
Advantages and Disadvantages of Small-Business Ownership
There are very few things in life that can compare to the experience of creating your own business. As investor and former entrepreneur James Caan expresses it: “Nothing will ever replace the thrill of creating a profitable company from scratch.”
Starting a small business is a matter of self-selection and self-determination. While the founders of small businesses still are a part of the society they live in, their business ventures can allow them to step into an alternate reality, part of a social order in which each person—regardless of gender, race, ethnicity, religion, birth or circumstances—can achieve their fullest potential and receive recognition for their achievements.
A small business owner has an extreme amount of latitude in both business and lifestyle choices, from developing the business concept and operating environment to defining success. The benefits—measured in impact, revenue, or infrastructure terms—are essentially unlimited. Perhaps the most nebulous, but important, benefit of being a small business owner is the freedom to choose your business’s purpose and goals.
The flip side is that you own the decisions and the results of those decisions. Evasion is not an option: you can’t say, “it’s not my job,” point fingers, shrug or check out. Additionally, as a small business owner, you will probably be risking your own (and, perhaps, friends & family) capital. Essentially, you’re flying without a net. There’s no guarantee of a regular paycheck and no paid or subsidized benefits (including a retirement plan, holidays, or perks). You’re responsible for business development, business planning, HR, IT, and every other function as well.
Freedom from an employer’s expectations comes at a cost: you’re responsible for setting and managing expectations—for yourself and others—and for making the magic happen.
practice question \(\PageIndex{1}\)
This section is a discussion of the advantages and disadvantages of starting a small business. According to the author, the underlying advantage to starting a small business is the freedom to make your own decisions regarding what the business is and what it does. But on the other side of the coin, the author reminds us that there is a price to pay- what is that price for the freedom from an employer’s expectation?
- The founder owns all of the responsibility for expectations and results.
- The founder sets the hours of operation for the business.
- The hounder is responsible for selecting employees
- The founder must maintain accurate records
- Answer
-
a. To be free of the expectations of an employer, the entrepreneur must accept the responsibility of self-expectation, as well as, the results of the business venture
Why Some Ventures Fail
Denbow’s point about the importance of planning is cited in virtually every list of causes of failure. Why is this so critical? Failure to do the research, analysis and financial projections that business planning entails makes a small business more vulnerable to the following common causes of failure:
- Inability to execute on the business concept
- Lack of or insufficient market demand
- Lack of product or service (competitive) differentiation & other marketing issues (the four Ps of marketing)
- Lack of awareness of and/or ability to respond to emerging trends, relevant developments (technology, regulatory, geo-political, environmental) and competitive actions
- Overdependence on a single customer
- Inability to manage growth
- Inadequate cash reserves or failure to effectively manage cash flows. Related point: inadequate cash controls or personal/business separation, including using business revenue as a personal slush fund
- Insufficient management experience or product/services expertise
- Lack of self-awareness and related personal/professional development
- An inability to acknowledge weakness and/or compensate for skill and expertise gaps
One of the most critical risk factors is the founder’s attitude and self-awareness, including the ability to objectively assess his or her management skills (or accept external feedback on this point), recruit to address skill and expertise gaps and effectively delegate responsibilities.
Statistics aside, it’s important to understand that failure isn’t final. The upside of failure is experience, a factor that contributes to success. Thus, the phrase “fail forward.” As Mike Maddock notes in his take-off on this concept: “the most inventive people are usually the best at failing forward, i.e., learning from what went wrong.”
practice question \(\PageIndex{2}\)
What are the underlying factors of the causes for small business failure?
- Government regulation
- Economic recession
- Failure to do the research, analysis and financial projections and the founder's attitude and self-awareness
- Failure to attract the right business partners
- Answer
-
c . According to the author, these are the most critical factors contributing to the various causes of small business failure.
Considerations When Starting a Business
The three fundamental questions to consider when deciding to start a business are:
- Do you have what it takes?
- Do you have a viable concept?
- Is the reason you want to start a business consistent with your character and concept?
Yourself
Do you have what it takes?
The entrepreneurial assessments discussed earlier this module are a good starting point for self-assessment. Additionally, you might want to take the Grit Test developed by psychology professor and researcher Angela Duckworth.
Another way to approach the question is to review the type of questions a founder might ask in an interview and consider whether you would hire yourself. For perspective, scan the questions —and thought process behind the questions—shared by startup leaders and others in Firstround.com’s The Best Interview Questions We’ve Ever Published. According to Anne Dwane, one of the serial entrepreneurs interviewed, “the most important quality any start-up leader (current or aspiring) can have is adaptability.” To get at that, she asks (and you might want to ask yourself – and reflect on your responses) the following questions:
- What have you started?
- How would you describe yourself in your own words?
- How would a colleague describe you in three adjectives?
- What current trends are you seeing in your profession? (Substitute your target industry/market for your profession)
- What new things have you tried recently?
Additional questions to consider include Koru co-founder and CEO Kristen Hamilton’s questions regarding grit, rigor, impact and ownership.
Your Concept
Do you have a viable concept?
Viability is something that will come out of the business planning process, which we will discuss in the next few sections. Before you dive into a business, it’s essential to do careful planning to ensure that the venture has potential to succeed. Jumping in with no information and no plan is a recipe for disaster.
Your Business
Is the reason you want to start a business consistent with your character and concept?
The third consideration is doing a reality check on why you want to start a business.  Can you connect the dots? Starting a new small business will require a lot of time and energy—if you’re not truly passionate about your venture, especially when it’s new, it (and you!) won’t be able to stand up to the stress of day-to-day business.
practice question \(\PageIndex{3}\)
Besides the importance of self-assessment (does the founder have what it takes) and matching the venture with the founder’s character (is the business consistent with what the founder wants to do), what is the third most-important element in deciding to start a small business?
- Conducting a self-interview
- Conducting a customer survey
- Conducting a business planning process to create a viable concept
- Conducting a reality check
- Answer
-
c. Besides the characteristics of the entrepreneur's personality and make up, conducting a rigorous planning process is vital to an informed decision to start a small business
Starting a business
Starting a business doesn’t have to be an all or nothing proposition. A number of successful entrepreneurs developed their business concepts while in school or working a traditional job. In his “The Surprising Habits of Original Thinkers” TED Talk, Organizational psychologist, professor and author Adam Grant discusses the mistake he made in passing on an opportunity to one of his student’s start-ups. He assumed that because the founders were working internships while developing the concept and had lined up jobs as a Plan B, they didn’t have the commitment to make the business a success.
The business the students launched: Warby Parker, a glasses e-tailer that Fast Company named as the world’s most innovative company in 2016. Warby Parker is currently valued at $1.75 million. For additional perspective, read Jason DeMers The Pros and Cons of Starting a Business While Working A Full-Time Job for Entrepreneur.


1.21: Discussion- Introduction to Retailing
Part 1
For this assignment, your task will be to interview somebody who is currently working in the retail industry. You might also choose somebody who has retired from the retail field. You can meet them in person or you might want to set up a time to talk on the phone. If it’s impossible to meet at the same time, you can email them these questions.
Ask at least four of the questions below:
- What is an average day like in your position?
- What are some of your primary functions?
- What are the benefits and drawbacks to working in retail?
- What is your role in the supply chain?
- How long have you been working in retail? Have you experienced/witnessed any major changes in retail during your career?
-
What career opportunities in retail do you see for someone interested in retail
marketing? - What advice do you have for someone who wants to be a manager?
Part 2
For each discussion forum, students need to create an initial post, then look over the discussion posts of your other classmates and give at least two (2) thoughtful responses to two (2) different classmates (one per classmate), totaling a minimum of three (3) posts for forum, including your initial post.
You need to write more than just a few words like: “I agree” or “Sounds good” or “Well said.” You must write several sentences that are thoughtful and suitable for a proper discussion. It is also fitting to ask questions or politely challenge your classmates if you like. When in doubt, just remember: this is a “discussion,” not a series of opinion blogs.
Grading Rubric
Your participation in this discussion will be graded using the following rubric. Please review and keep it in mind as you prepare your assignment.
| Criteria | Not Evident | Developing | Exemplary | Points |
|---|---|---|---|---|
| Submit initial response |
0 pts
No response |
2 pts
Response does not fully address the prompt |
5 pts
Response thoughtfully addresses the prompt and invites response from peers. |
5 pts |
| Respond to at least two peers |
0 pts
No response to peers |
2
pts
Responded to only one peer |
5 pts
Responded to at least two peers |
5 pts |
| Total: | 10 pts |
Contributors and Attributions
- Discussion: Introduction to Retailing. Provided by : Lumen Learning. License : CC BY: Attribution
- Revision and adaptation. Authored by : Jameson Gurley. Provided by : Lumen Learning. License : CC BY: Attribution


3.1: Every Network is an Island
Navigating your path through the terrain of social media marketing can seem daunting, particularly when deciding which social media platform is most suitable for your business. You’ve defined your objectives; you may be aiming to hone your skills as a social media marketer for an enterprise or leveraging your knowledge to boost your startup’s growth. In either scenario, the question of “Which social media platform is the best for my business?” inevitably arises.
This is a longstanding debate, yet it’s important to realize that each network carries its own significance. The choice of platform hinges not on general perceptions of ‘the best’, but on what best aligns with your unique business goals and fits the specific needs of your customer personas.
Social media platforms were developed with distinct objectives in mind. Facebook sought to unify individuals worldwide, LinkedIn established an avenue for professional networking, Instagram provided a platform for all age groups to capture and chronicle their significant moments. Consequently, understanding the benefits unique to each platform is vital. It’s about deciding which platform offers the capabilities that best serve your business goals, aligns with your industry and resonates with your defined customer personas.
Remember the initial chapters: “What business are you in?” and “Who is your customer?” Keeping your specific industry and your target customer personas in mind is key when assessing these platforms. Each one offers unique benefits and reaches specific demographics, so consider where your customers are most likely to be active and engaged. The platform that best reaches your customers and aligns with your business objectives is the one you want to focus on.
Regardless of whether you’re a budding startup or an established brand, it’s wise to secure your brand name across all social media networks, even if you’re not actively using them in your current strategy. This preemptive measure ensures your brand name isn’t hijacked or misused by others.
Who Lives There?
A primary appeal of social media for marketers is the extensive targeting options it provides. Unlike traditional marketing which often focuses on mass marketing, social media marketing allows you to precisely target the audience for your marketing campaigns.
Before launching any marketing campaign, it’s essential to set clear goals, including defining the type of audience who should view your ads and how they should interact with your business. For this, it’s essential to know the demographics of users on each social platform. Let’s talk Statistics for a bit.
Find more statistics at Statista
Facebook is populated mostly by adults of 25-34 years age group. The second largest group is 18-24 years who make up 23.8% of Facebook’s population and only 4.8% of users fall into the senior age group. The biggest country present on the platform is India, while users from the US and Canada are only 10% of the total Facebook population. As for gender, males dominate the platform with 56% of the total population. Also, 51% active users visit the website several times a day and 75% of Facebook users are at least college graduates.
On Instagram, the highest population is of 25-34 year olds who make up 33.1% of all users and age group of 18-24 years is second with 29.6% share. Most of them come from the US, whereas India and Brazil hold second and third positions respectively. 43% of these users are college graduates and 42% earn over $75,000 per annum.
Over 510 million users are females and males are behind with a difference of 20 million. These users spend around 28 minutes a day on Insta. Most users follow at least a single brand on the app and 73% of teens in the US find Instagram the easiest way to reach and interact with a brand.
TikTok
TikTok is a customer favorite app and stands second among the most popular free apps of 2019. Its users are present in 141 countries while China, India, United States, and Turkey are among the countries where it is more frequently downloaded and used.
44% TikTok users are females and 56% are males. Out of these, 41% users are aged 16-24 years who spend at least 52 minutes every day on the app, watching videos related to entertainment, dance, pranks, fitness and other categories.
90% of TikTok or Douyin users access the app via Android smartphones and maintain a healthy engagement rate of 52%. In 2019, people spent $115.3 million on the app for in-app purchases, influencer marketing, etc.
This was a brief overview of some popular social platforms. You can opt for the platform that suits your business needs.
What Language Do They Speak?
Whether you’re talking to friends in a party, communicating with little kids in social gatherings, or sharing thoughts with business associates in a professional setting, you should always be aware of your audience. When you choose the language or tone they understand, you can conveniently communicate with each other without misunderstandings.
Don’t forget this rule when communicating with your audience on social media. Creating a profile on social websites is easy. What’s difficult is to spread your message and get people talking about the brand in a positive manner. However, this objective can be achieved by determining what type of content the audience prefers and creating posts accordingly.
Hashtags (#)
Hashtags were introduced by Chris Messina in an attempt to organize content on social media. Twitter platform first introduced this unique feature in 2007, but it was later adopted by Facebook, Instagram, YouTube, Pinterest, and LinkedIn due to its usability.
A hashtag categorizes content on the basis of topic. If you want to reach the right audience for your business, you need to target popular and relevant ones. Moreover, you can also create custom hashtags to promote your products.
Let’s discuss this concept with an example. Imagine that a roofing service provider hires you as a social media marketer. To build their business online, you need to come up with suitable hashtags for the social marketing strategy. Here are a few trends and hashtags that may prove useful:
#roofing #roofingcontractor #construction #greenroofing #roofrepair #roofgutters
Long Form vs. Short Form Content
The internet users tend to have short attention spans. They easily get distracted and can ignore your posts if they don’t find it interesting. This is why content marketing in digital media focuses on captivating and concise content that can keep readers hooked till the last line.
If we need to keep the content short, how can we share important information or news with the target audience?
It’s common for social media marketers to get confused about the length of content. But you should remember that the content length depends on the interest of your audience as well as the platform where you intend to post it.
If you are planning to set up a company blog, it’s best to opt for long-form content. The purpose of blogging is to educate people about a relevant topic and offer comprehensive solutions to problems. For example, if you are an expert in providing electrical installation and repair services, you may want to write posts about safety tips for customers. Blog posts can be 500-1,000 words, but you should aim for publishing blogs of 2,000-2,500 words to boost SEO score.
LinkedIn is also suitable for posting long-form content. You can write about your area of expertise and experiences to share knowledge with other professionals.
Other social platforms such as Facebook, Twitter, Instagram, etc. may be suitable for short-term content. Whether you are thinking of creating text posts, videos, or images, it’s a better option to keep the content short for better engagement.
Also, don’t forget that long form videos aren’t compatible with most social websites. Instagram supports videos of up to 15 seconds. So, if you are creating long form informative videos, it may be a good option to post it on YouTube and share a brief snippet on Twitter and other social websites. Your followers who find the topic interesting will visit your YouTube channel to watch the entire video.
What’s Their Favorite Dish?
Back in the day, social media marketing was all about text posts and still images. With technology advancements, a wide variety of content is now available to internet users. Let’s first take a look at the most popular types of digital content. After that, we will discuss which content goes well with popular social websites.
- Blogs or articles
- eBooks
- Images (still images, GIFs, 360° images)
- Videos (recorded videos and live streaming)
- Infographics
- Testimonials
- Contests
- Polls
- Podcasts
- Webinars
- How-to guides
Instagram is an image-based platform. To promote your brand, you can share high-quality images of products, team members, as well as stills from networking events. Adding relevant captions and hashtags is also essential. A similar strategy is suitable for Pinterest where you can capture attention via images.
As for Facebook , videos perform far better than any other type of content. This includes live streams as well as processed images for coverage of organizational events. You can also post videos developed with the aim of advertising on your Facebook page.
With the increasing population of TikTok , you shouldn’t ignore its importance in the marketing plan. You can complement videos with captions and can include links to your website to increase web traffic.
Twitter network is known for its credibility when it comes to news and information. Users of this platform show more interest in professionally processed content which includes informational infographics and videos.
For LinkedIn , you can turn to long form articles, user guides, and eBooks to increase engagement. We all know YouTube is one of the most popular video streaming websites. So, you can post videos on this platform regardless of their size or length.
https://www.oberlo.com/blog/social-media-marketing-statistics


5.0: Introduction
The jump from arithmetic to algebra can be a difficult one for many students. Many students struggle with the idea that mathematics can include situations that aren’t static and do change. In elementary arithmetic, a situation such as:
is a static situation and will yield the answer of 8 every time. However, a situation such as:
can yield many different answers because the answer depends on what amount (number) that represents. Since the value of can vary (represent different values), it is known as a variable.
Algebra is useful to better model real life situations. In the first equation shown, can only model situations where you add those two numbers together.  The second equation can model more complex situations. For example, you wish to buy a game that costs $38 but you only have three dollars. Your uncle will pay you five dollars an hour to work for him. If you’ve worked five hours, have you earned enough money? If not, how many hours will you have to work?
Algebra and algebraic thinking open up a world of possibilities that arithmetic alone cannot do.


10.1: Plant Diversity Imbalance
The diversity of flowering plants (the angiosperms) dwarfs the number of species of their closest evolutionary relatives (Figure 10.1). There are more than 260,000 species of angiosperms (that we know; more are added every day). The clade originated more than 140 million years ago (Bell et al. 2005) , and all of these species have formed since then. One can contrast the diversity of angiosperms with the diversity of other groups that originated at around the same time. For example, gymnosperms, which are as old as angiosperms, include only around 1000 species, and may even represent more than one clade. The diversity of angiosperms also dwarfs the diversity of familiar vertebrate groups of similar age (e.g. squamates - snakes and lizards - which diverged from their sister taxon, the tuatara, some 250 mya or more Hedges et al. 2006, include fewer than 8000 species) .
The evolutionary rise of angiosperm diversity puzzled Darwin over his career, and the issues surrounding angiosperm diversification are often referred to as “Darwin’s abominable mystery” in the scientific literature (e.g. Davies et al. 2004) . The main mystery is the tremendous variation in numbers of species across plant clades (see Figure 10.1). This variation even applies within angiosperms, where some clades are much more diverse than others.
At a global scale, the number of species in a clade can change only via two processes: speciation and extinction. This means that we must look to speciation and extinction rates – and how they vary through time and across clades – to explain phenomena like the extraordinary diversity of Angiosperms. It is to this topic that we turn in the next few chapters. Since Darwin’s time, we have learned a lot about the evolutionary processes that led to the diversity of angiosperms that we see today. These data provide an incredible window into the causes and effects of speciation and extinction over macroevolutionary time scales.
Comparative methods can be applied to understand patterns of species richness by estimating speciation and extinction rates, both across clades and through time. In this chapter, I will introduce birth-death models, by far the most common model for understanding diversification in a comparative framework. I will discuss the mathematics of birth-death models and how these models relate to the shapes of phylogenetic trees. I will describe how to simulate phylogenetic trees under a birth-death model. Finally, I will discuss tree balance and lineage-through-time plots, two common ways to measure the shapes of phylogenetic trees.


In this chapter, we explore several problems in geometric probability. These problems are interesting, conceptually clear, and the analysis is relatively simple. Thus, they are good problems for the student of probability. In addition, Buffon's problems and Bertrand's problem are historically famous, and contributed significantly to the early development of probability theory.
-
-
10.1: Buffon's Problems
-
Buffon's experiments are very old and famous random experiments, named after comte de Buffon. These experiments are considered to be among the first problems in geometric probability.
-
-
10.2: Bertrand's Paradox
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Bertrand's problem is to find the probability that a random chord on a circle will be longer than the length of a side of the inscribed equilateral triangle. The problem is named after the French mathematician Joseph Louis Bertrand, who studied the problem in 1889.
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10.3: Random Triangles
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Suppose that a stick is randomly broken in two places. What is the probability that the three pieces form a triangle?


2.5.1: Four Representations
Lesson
Let's contrast relationships that are and are not proportional in four different ways.
Exercise \(\PageIndex{1}\): Which is the Bluest?
1. Which group of blocks is the bluest?
2. Order the groups of blocks from least blue to bluest.
Exercise \(\PageIndex{2}\): One Scenario, Four Representations
-
Select two things from different lists. Make up a situation where there is a
proportional relationship
between quantities that involve these things.
-
creatures
- starfish
- centipedes
- earthworms
- dinosaurs
-
length
- centimeters
- cubits
- kilometers
- parsecs
-
time
- nanoseconds
- minutes
- years
- millennia
-
volume
- milliliters
- gallons
- bushels
- cubic miles
-
body parts
- legs
- eyes
- neurons
- digits
-
area
- square microns
- acres
- hides
- square light-years
-
weight
- nanograms
- ounces
- deben
- metric tonnes
-
substance
- helium
- oobleck
- pitch
- glue
-
creatures
- Select two other things from the lists, and make up a situation where there is a relationship between quantities that involve these things, but the relationship is not proportional.
-
Your teacher will give you two copies of the “One Scenario, Four Representations” sheet. For each of your situations, describe the relationships in detail. If you get stuck, consider asking your teacher for a copy of the sample response.
- Write one or more sentences describing the relationship between the things you chose.
- Make a table with titles in each column and at least 6 pairs of numbers relating the two things.
- Graph the situation and label the axes.
- Write an equation showing the relationship and explain in your own words what each number and letter in your equation means.
- Explain how you know whether each relationship is proportional or not proportional. Give as many reasons as you can.
Exercise \(\PageIndex{3}\): Make a Poster
Create a visual display of your two situations that includes all the information from the previous activity.
Summary
The constant of proportionality for a proportional relationship can often be easily identified in a graph, a table, and an equation that represents it. Here is an example of all three representations for the same relationship. The constant of proportionality is circled:
On the other hand, some relationships are not proportional. If the graph of a relationship is not a straight line through the origin, if the equation cannot be expressed in the form \(y=kx\), or if the table does not have a constant of proportionality that you can multiply by any number in the first column to get the associated number in the second column, then the relationship between the quantities is not a proportional relationship.
Practice
Exercise \(\PageIndex{4}\)
The equation \(c=2.95g\) shows how much it costs to buy gas at a gas station on a certain day. In the equation, \(c\) represents the cost in dollars, and \(g\) represents how many gallons of gas were purchased.
- Write down at least four (gallons of gas, cost) pairs that fit this relationship.
- Create a graph of the relationship.
- What does 2.95 represent in this situation?
- Jada’s mom remarks, “You can get about a third of a gallon of gas for a dollar.” Is she correct? How did she come up with that?
Exercise \(\PageIndex{5}\)
There is a proportional relationship between a volume measured in cups and the same volume measured in tablespoons. 3 cups is equivalent to 48 tablespoons, as shown in the graph.
- Plot and label at least two more points that represent the relationship.
- Use a straightedge to draw a line that represents this proportional relationship.
- For which value y is \((1,y)\) on the line you just drew?
- What is the constant of proportionality for this relationship?
- Write an equation representing this relationship. Use \(c\) for cups and \(t\) for tablespoons.


17.3: Pharmacological Pain Management
By the end of this section, you will be able to:
- Provide patient education on, administer, and monitor patients receiving analgesic medications during the process of labor and birth
- Educate the patient desiring nitrous oxide for the discomfort of labor and birth
- Explain the role of naloxone during the process of labor and birth
The laboring person determines the level of pain they are experiencing during labor. Every person has a different level of pain tolerance and should be able to request pain relief measures at any time during labor. Analgesia refers to the inability to feel pain, and the medications designed to lessen or eliminate pain without loss of consciousness are called analgesics. For persons desiring analgesia in labor, many safe options are available. The nurse provides education on different types of analgesics, their side effects, and what monitoring is required while using the analgesic. The nurse administers the analgesics as prescribed and monitors and documents the effectiveness per facility protocol.
Analgesia
Analgesia is used often for labor pain. It is important to note that all analgesics cross the placenta. Most analgesics cause a depressant effect on the laboring person and the fetus; therefore, the nurse will assess the FHR, vital signs, cervical dilation, and stage of labor prior to administering pain medication. Analgesics can be administered by many different routes: subcutaneous, intramuscular, intravenous, inhaled, and oral. In most cases, analgesics are administered intravenously (IV). This route allows faster pain relief to the laboring person. This route, however, causes a depressant effect; if too high a dose is given, it can lead to respiratory depression . Intravenously administered analgesics reach the fetus quickly and stay in the fetal system longer. If the fetus is born while the analgesic is still circulating, the fetus can exhibit depressed respirations.
Analgesia can be divided into categories. Table 17.2 lists the categories and some examples of analgesia.
| Category of Analgesia | Description | Medications |
|---|---|---|
| Tranquilizer/Amnestic |
Relieves anxiety
Rapid sedation |
Hydroxyzine (Vistaril) |
| Narcotic |
Relieves pain
Reduces anxiety Causes respiratory depression |
Fentanyl |
| Ultra-short-acting synthetic opioid |
Relieves pain
Causes respiratory depression Rapidly metabolized Does not accumulate in the fetus |
Remifentanil (Ultiva) |
| Opioid agonist-antagonist |
Relieves pain
Less respiratory depression |
Butorphanol (Stadol)
Nalbuphine (Nubain) |
| Inhaled analgesic |
Reduces anxiety
Reduces pain Rapidly reversed |
Nitrous oxide (50% N 2 O/50% O 2 ) |
Hydroxyzine
Hydroxyzine (Vistaril) is an anxiolytic that causes drowsiness and creates a feeling of calm. Hydroxyzine is commonly used in latent or early labor to relieve anxiety and allow the person to rest until active labor begins. It is not normally used during active labor. Hydroxyzine also has antihistamine properties that can cause drowsiness to aid in sleep. Side effects include dry mouth, constipation, dizziness, and headache (Brunton & Knollman, 2022). Hydroxyzine can be administered orally and intramuscularly. The nurse educates the pregnant person that they will feel relaxed and sleepy but that hydroxyzine is not a pain reliever. If the person begins to experience labor pain, they should ask the nurse what the health-care provider has ordered for pain relief.
Promethazine
Promethazine (Phenergan) is an antiemetic that is given for nausea and vomiting or in conjunction with a narcotic. It causes drowsiness and can help the laboring person sleep. Nausea and vomiting are common discomforts in labor, and promethazine can be used as treatment. Promethazine’s side effects include drowsiness, nervousness, restlessness, and dry mouth (Brunton & Knollman, 2022). Routes include oral, rectal, intramuscular (IM), and intravenous (IV). The nurse should be aware of the caustic nature of the medication and should give IM injections deep into the muscle. When administering promethazine IV push, the medication should be diluted adequately (usually with 5 to 10 mL of normal saline) and administered slowly (over 5 to 10 minutes). The nurse educates the laboring person on the side effects and encourages the person to ask for assistance when getting out of bed.
Butorphanol
Butorphanol (Stadol) is an opioid agonist-antagonist used for moderate to severe pain in labor. It can be given intramuscularly or intravenously. It causes sedation and decreased pain. Side effects include dizziness, confusion, nausea, constipation, respiratory depression, and withdrawal syndrome (Brunton & Knollman, 2022). Because of the medication’s antagonist property, persons dependent on opiates can have withdrawal symptoms when taking butorphanol. The nurse should assess the person’s social history prior to administering the medication. The nurse educates the laboring person and partner on the side effects and explains the need for assistance when getting out of bed.
Nalbuphine
Nalbuphine (Nubain) is an opioid agonist-antagonist used for moderate to severe pain in labor. Side effects include dizziness, nausea, respiratory depression, and urinary retention (Brunton & Knollman, 2022). It should not be given to persons with substance use disorder, as it can precipitate withdrawal. It is normally given intramuscularly or intravenously, but can also be administered subcutaneously. As with butorphanol, the nurse must assess the person’s social history regarding opioid dependency and signs of opioid withdrawal prior to administering. The nurse explains the side effects and encourages the person to call for assistance when getting out of bed.
Fentanyl
Fentanyl is a potent opioid used to treat moderate to severe pain. It can be administered through an epidural catheter or intravenously. Side effects include nausea, bradycardia, hypotension, sedation, peripheral vasodilation, and potentially fatal respiratory depression (Brunton & Knollman, 2022). Some institutions require a continuous pulse oximeter to be used to monitor oxygen saturation while using this opioid. The nurse should keep an opioid antagonist readily available in case of overdose and respiratory depression. The nurse educates the laboring person and partner on the side effects and the importance of calling for assistance when getting out of bed.
Pain Relief Expectations
The beliefs and perceptions of the person experiencing childbirth influence their subjective labeling and response to the process of labor and birth as well as any decisions made within the health-care setting. Pain is part of the labor and birth process, and culture influences a person’s perception and communication of their pain. Laboring persons of various cultures may express their pain by vocalization or no expression at all and, when asked what their level of pain is, may state the pain is a low level. Culture or individual choice will dictate what the person chooses to relieve the pain and discomfort of the labor and birth process. These choices are based on the interaction of psychologic, social, and physiologic factors. Understanding and respecting individual choices for pain relief is essential to culturally competent nursing care (Mousa et al., 2018).
 N 2 O is used for labor analgesia in all stages of labor and is safe for the laboring person and the fetus. N 2 O does not cause a sedating effect on the fetus, as narcotic analgesia does, and has a rapid onset and clearance. The safe concentration for labor analgesia is 50% N 2 O to 50% oxygen. A machine permanently set at this setting is used to blend the gases; the setting cannot be changed. The gas is inhaled through a mask held only by the laboring person. The gas is not free flowing. The person must place the mask firmly against the face to develop negative pressure to inhale the gas. The laboring person is in control of how much and how often to use the gas. Laboring persons describe feeling relaxed with mild pain relief. The common side effects are nausea, vomiting, and dizziness. The nurse educates the person and support person that the mask must be held only by the laboring person, the gas takes several breaths to become effective, and the person must breathe through the contractions to make it effective. Opioids used in conjunction with N 2 O can cause an increased risk for respiratory depression and are therefore not recommended.
Naloxone
Naloxone ( Narcan ) is the antidote to opioids. It rapidly replaces opioids by binding to opioid receptors and blocking the opioid from reattaching. This reverses the respiratory depression caused by opioid overdose. On the labor and delivery unit, naloxone is readily available because of the narcotics being administered for pain relief. Naloxone can be administered to the laboring person if their respirations are shallow or their oxygen saturation is low (Vallerand & Sanoski, 2023). It can be given to the newborn if respirations are slow, crying is weak, or color is poor. Opioids rapidly cross the placenta and enter the fetal circulation. If the opioid has not metabolized and cleared from the fetal circulation, the newborn can experience respiratory depression. In this case, the newborn may be given naloxone to reverse the opioid-related respiratory depression. If the birthing person is opioid dependent, naloxone should not be administered to the newborn due to possible seizure activity. The nurse monitors for respiratory depression in the laboring person, newly delivered person, and neonate when naloxone is administered.


7.2: Elbow Joint
The elbow joint is a uniaxial hinge joint formed by the humeroulnar joint , the articulation between the trochlea of the humerus and the trochlear notch of the ulna. Also associated with the elbow are the humeroradial joint and the proximal radioulnar joint. All three of these joints are enclosed within a single articular capsule (Figure \(\PageIndex{1}\)).
The articular capsule of the elbow is thin on its anterior and posterior aspects, but is thickened along its outside margins by strong intrinsic ligaments. These ligaments prevent side-to-side movements and hyperextension. On the medial side is the triangular ulnar collateral ligament. This arises from the medial epicondyle of the humerus and attaches to the medial side of the proximal ulna. The strongest part of this ligament is the anterior portion, which resists hyperextension of the elbow. The ulnar collateral ligament may be injured by frequent, forceful extensions of the forearm, as is seen in baseball pitchers. Reconstructive surgical repair of this ligament is referred to as Tommy John surgery, named for the former major league pitcher who was the first person to have this treatment.
The lateral side of the elbow is supported by the radial collateral ligament. This arises from the lateral epicondyle of the humerus and then blends into the lateral side of the annular ligament. The annular ligament encircles the head of the radius. This ligament supports the head of the radius as it articulates with the radial notch of the ulna at the proximal radioulnar joint. This is a pivot joint that allows for rotation of the radius during supination and pronation of the forearm.


5.5: Patient Rights
When individuals with mental health disorders are admitted to a hospital, they may lose a number of abilities that we take for granted, such as the ability to come and go, schedule their time, and choose and control their activities of daily living. In many states, patients’ rights associated with inpatient admission to a mental health unit are spelled out in state law. Patients must be specifically informed of their rights as described in the Patient Bill of Rights document.
Clients who are determined to be legally incompetent also lose the ability to manage their financial and legal affairs and make important decisions. The Patient Self-Determination Act was passed to protect patient rights. [1]
The Patient Self-Determination Act was passed in 1990 and is considered a landmark law for patient rights. This law requires hospitals, skilled nursing facilities, home health agencies, hospice programs, and health maintenance organizations to provide clear written information for patients concerning their legal rights to make health care decisions, including the right to accept or refuse treatment. It also requires agencies to ask patients about advanced directives and to document any wishes the patient has in regard to the care they do or do not want. [2] Interprofessional team members, including nurses, have an ethical duty to ensure that patients know and understand their health care-related rights. [3] See the following box for a list of patient rights included in this law. These rights are further discussed in the following subsections.
Patient Self-Determination Act [4]
- The right to appropriate treatment and related services in a setting and under conditions that are the most supportive of a person’s personal liberty and restrict such liberty only to the extent necessary consistent with the person’s treatment needs, applicable requirements of law, and applicable judicial orders.
- The right to an individualized, written treatment or service plan (developed promptly after admission), the right to treatment based on the plan, the right to periodic review and reassessment of treatment and related service needs, and the right to appropriate revision of the plan, including revisions necessary to provide a description of mental health services that may be needed after the person is discharged from the program or facility.
- The right to ongoing participation, in a manner appropriate to the person’s capabilities, in the planning of mental health services to be provided (including the right to participate in the development and periodic revision of the plan).
- The right to be provided with a reasonable explanation, in terms and language appropriate to the person’s mental and physical condition, the objectives of treatment, the nature and significance of possible adverse effects of recommended treatment, the reasons why the recommended treatment is considered appropriate, the reasons why access to certain visitors may not be appropriate, and any appropriate and available alternative treatments, services, and types of providers of mental health services.
- The right not to receive a course of treatment in the absence of informed, voluntary, written consent to treatments except during an emergency situation or as permitted by law when the person is being treated as a result of a court order.
- The right to not participate in experimentation in the absence of informed, voluntary, written consent.
- The right to freedom from restraint or seclusion, other than as a course of treatment during an emergency situation with a written order by a mental health professional.
- The right to a humane treatment environment that affords reasonable protection from harm and appropriate privacy with regard to personal needs.
- The right to access, on request, one’s mental health care records.
- The right of a person admitted to residential or inpatient care to converse with others privately, to have convenient and reasonable access to the telephone and mail, and to see visitors during regularly scheduled hours.
- The right to be informed promptly at the time of admission and in writing of these rights.
- The right to assert grievances with respect to infringement of these rights.
- The right to exercise these rights without reprisal.
- The right of referral to other providers upon discharge.
Informed Consent
Informed consent is the fundamental right of an individual to accept or reject health care. Based on the Patient Self-Determination Act, clients have the right to give informed consent before receiving medical assessment or treatment (except in emergency situations when imminent harm may occur to themselves or others). Most states allow a client to sue for battery if consent is not obtained before medical treatment is given. [5] However, a client must be competent and have the legal capacity to give informed consent.
Competency is a legal term related to the degree of cognitive ability an individual has to make decisions or carry out specific acts. Individuals are considered competent until they have been declared incompetent in a formal legal proceeding. If found incompetent, the individual is appointed a legal guardian or representative who is responsible for providing or refusing consent (while considering the individual’s wishes). Guardians are typically family members such as spouses, adult children, or parents. If family members are unavailable or unwilling to serve in this role, the court may appoint a court-trained guardian. [6]
Capacity is a functional determination that an individual is or is not capable of making a medical decision within a given situation. It is outside the scope of practice for nurses to formally assess capacity, but nurses may initiate the evaluation of client capacity and contribute assessment information. Capacity may be a temporary or permanent state. The following box outlines situations where the nurse may question a client’s decision-making capacity. [7] , [8]
Triggers for Questioning a Client’s Decision-Making Capacity
- Unawareness of surroundings
- Absence of questions about the treatment being offered or provided
- New inability to perform activities of daily living
- Disruptive behavior or agitation
- Labile emotions
- Hallucinations
- Intoxication
When a client does not have the capacity to provide informed consent, health care providers must obtain substituted consent for treatments. Substituted consent is authorization that another person gives on behalf of the patient. For example, the activation of a client’s health care power of attorney is an example of substituted consent. Substituted consent may also come from a court-appointed guardian or if state law permits, from next of kin. [9]
Read more about informed consent and capacity in the “ Other Legal Issues ” section of Open RN Nursing Management and Professional Concepts .
Protective Placement
Guardianships and protective orders are legal methods in states for appointing an alternative decision-maker and identifying required services for individuals who are legally incompetent.  A court can issue orders for a person who has a guardian to be protectively placed. The legal standard basically states that without the protective placement, the individual is so incapable of providing for their own care and well-being that it creates a substantial risk of serious harm to themselves or others. Protective services may include case management, in-home care, nursing services, adult day care, or inpatient treatment. Protective placements must be the least restrictive setting necessary to meet the individual’s needs and must be reviewed annually by the court.
Psychiatric Advance Directive
A Psychiatric Advance Directive (PAD) is a legal document that describes a person’s preferences for future mental health treatment or names an individual to make treatment decisions for them if they are in a crisis and unable to make decisions. Many people with mental illness, their family members, and health professionals are not familiar with PADs. [10]
For states that do not have laws regarding PADs, an individual can still draft a PAD under the more general statutes connected to advance health care directives and living wills. However, a PAD is more beneficial because of the unique issues of mental health care and treatment, such as medication preferences and inpatient treatment considerations and the fact that a person with mental health disorders can experience recovery and wellness over time. [11]
Read more about Psychiatric Advance Directives on the National Alliance on Mental Illness website.
Restraints and Seclusion
Restraints are devices used in health care settings to prevent patients from causing harm to themselves or others when alternative interventions are not effective. A restraint is a device, method, or process that is used for the specific purpose of restricting a patient’s freedom of movement without the permission of the person. Restraints include mechanical devices such as a tie wrist device, chemical restraints, or seclusion. The Joint Commission defines a chemical restraint as a drug used to manage a patient’s behavior, restrict the patient’s freedom of movement, or impair the patient’s ability to appropriately interact with their surroundings that is not standard treatment or dosage for the patient’s condition. [12] It is important to note that the definition states the medication “is not standard treatment or dosage for the patient’s condition.” For example, administering prescribed benzodiazepines as standard treatment to manage the symptoms of a diagnosed mental health disorder is not considered a chemical restraint, but administering benzodiazepines to limit a patient’s movement is considered a chemical restraint.
Seclusion is defined as the confinement of a patient in a locked room or an area from which they cannot exit on their own. Seclusion should only be used for the management of violent or self-destructive behavior. Seclusion limits freedom of movement because, although the patient is not mechanically restrained, they cannot leave the area. [13] , [14]
Although restraints are used with the intention to keep a patient safe, they impact a patient’s psychological safety and dignity and can cause additional safety issues and death. A restrained person has a natural tendency to struggle and try to remove the restraint and can fall or become fatally entangled in the restraint. Furthermore, immobility that results from the use of restraints can cause pressure injuries, contractures, and muscle loss. Restraints take a large emotional toll on the patient’s self-esteem and may cause humiliation, fear, and anger.
Restraint Guidelines
The American Nurses Association (ANA) has established evidence-based guidelines that a restraint-free environment is the standard of care. The ANA encourages the participation of nurses to reduce patient restraints and seclusion in all health care settings. Restraining or secluding patients is viewed as contrary to the goals and ethical traditions of nursing because it violates the fundamental patient rights of autonomy and dignity. However, the ANA also recognizes there are times when there is no viable option other than restraints to keep a patient safe, such as during an acute psychotic episode when patient and staff safety are in jeopardy due to aggression or assault. The ANA also states that restraints may be justified in some patients with severe dementia or delirium when they are at risk for serious injuries such as a hip fracture due to falling. [15]
The ANA provides the following guidelines: “When restraint is necessary, documentation should be done by more than one witness. Once restrained, the patient should be treated with humane care that preserves human dignity. In those instances where restraint, seclusion, or therapeutic holding is determined to be clinically appropriate and adequately justified, registered nurses who possess the necessary knowledge and skills to effectively manage the situation must be actively involved in the assessment, implementation, and evaluation of the selected emergency measure, adhering to federal regulations and the standards of the The Joint Commission (2009) regarding appropriate use of restraints and seclusion.” Nursing documentation typically includes information such as patient behavior necessitating the restraint, alternatives to restraints that were attempted, the type of restraint used, the time it was applied, the location of the restraint, and patient education regarding the restraint. [16]
Any health care facility that accepts Medicare and Medicaid reimbursement must follow federal guidelines for the use of behavioral restraints. These guidelines include the following [17] :
- When a restraint is the only viable option, it must be discontinued at the earliest possible time.
- Orders for the use of seclusion or restraint can never be written as a standing order or PRN (as needed).
- The treating physician must be consulted as soon as possible if the restraint or seclusion is not ordered by the patient’s treating physician.
- A physician or licensed independent practitioner must see and evaluate the need for the restraint or seclusion within one hour after the initiation.
- After restraints have been applied, the nurse should follow agency policy for frequent monitoring and regularly changing the patient’s position to prevent complications. Nurses must also ensure the patient’s basic needs (e.g., hydration, nutrition, and toileting) are met. Range of motion exercises and circulatory checks are typically provided hourly. Some agencies require a 1:1 patient sitter or continuous monitoring when restraints are applied or seclusion is implemented.
- Each written order for a physical restraint or seclusion is limited to 4 hours for adults, 2 hours for children and adolescents ages 9 to 17, or 1 hour for patients under 9. The original order may only be renewed in accordance with these limits for up to a total of 24 hours. After the original order expires, a physician or licensed independent practitioner (if allowed under state law) must see and assess the patient before issuing a new order.
Review safe use of restraints and alternatives to restraints in the “ Restraints ” section of the “Safety” chapter in Open RN Nursing Fundamentals .
Admission for Care
When clients with mental health disorders are admitted for inpatient care, the type of admission dictates certain rights and aspects of their treatment plan. Admissions may be voluntary admissions, emergency admissions, or involuntary admissions.
Voluntary Admission
Individuals over age 16 who present to a psychiatric facility and request hospitalization are considered voluntary admissions . Clients admitted under voluntary admission have certain rights that differ from emergency and involuntary admissions. For example, they are considered competent with the capacity to make health care decisions (unless determined otherwise). Therefore, they have the right to refuse treatment, including psychotropic medications, unless they become a danger to themselves or others. [18]
Clients with voluntary admission do not necessarily have an absolute right to discharge at any time but may be required to request discharge. This gives the health care team an opportunity to initiate a procedure to change the client’s admission status to involuntary if needed and associated legal requirements are met. [19]
Emergency Admissions
Many states allow individuals to be admitted to psychiatric facilities under emergency admission status when they are deemed likely to harm themselves or others. State laws define the exact procedure for the initial evaluation, possible length of detainment, and treatment provided. All clients who are admitted as emergency admissions require diagnosis, evaluation, and emergency treatment according to state law. At the end of the admission period, the facility must either discharge the patient, change their status to voluntary admission, or initiate a civil court hearing to determine the need for continuing treatment on an involuntary basis. [20]
During an emergency admission, the client’s right to come and go is restricted, but they have a right to consult with an attorney and prepare for a hearing. Clients may be forced to receive psychotropic medications if they continue to be a danger to themselves or others. However, invasive procedures like electroconvulsive therapy (ECT) are not permitted unless they are ordered by the court or consented to by the client or their legal guardian. [21]
Involuntary Admissions
There may be circumstances when a person becomes so mentally ill they are at risk of hurting themselves or others, and involuntary admission for care becomes necessary even though the individual does not desire care. An individual can have an involuntary admission to a psychiatric facility if they are diagnosed with a mental illness, pose a danger to themselves or others, are gravely disabled (e.g., unable to provide themselves basic necessities like food, clothing, and shelter), or are in need of treatment but their mental illness prevents voluntary help-seeking behaviors. The legal procedures are different in each state, but standards for involuntary admission are similar. [22] , [23]
Because involuntary commitment is a serious matter, there are strict legal protections established by the U.S. Supreme Court. The standard of proof of “mentally ill and dangerous to self or others” must be based on “clear and convincing evidence.” Therefore, two physicians must certify the individual’s mental health status. Additionally, the client has the right to legal counsel and can take the case to a judge who can order release. If not released, the client can be involuntarily committed to a state-specified number of days with interim court appearances. Most states permit a 72-hour admission followed by a formal hearing. If the client feels they are being held without just cause, they can file a writ of habeas corpus (i.e., a formal written order to free the person). The court makes a decision based on the “least restrictive alternative” doctrine, meaning the least drastic action is taken to achieve the purpose of care. [24] , [25] Review your state’s laws regarding involuntary admissions.
For example, Wisconsin state law, referred to as “ Chapter 51 ,” dictates the requirements for involuntary admissions and is further explained by NAMI Kenosha County .
Involuntary Admission of Minors
Special considerations apply to minors receiving psychiatric care. Many states grant minors aged 12-18 the right to provide consent for mental health treatment and to protest involuntary admission unless they are a risk to themselves or others. In many cases, a neutral mental health review officer is assigned to the case to ensure rights are upheld. [26] State laws are complex; therefore, nurses must be aware of legal protections of minors in the state in which they work.
Read additional information about Clients’ Rights for Minors in Wisconsin.
Criminal Cases and Pleas of Insanity
If a defendant pleads an insanity defense in a criminal case, they are involuntarily admitted to a mental health facility for an evaluation period determined by state law. During this time an interprofessional team of mental health professionals (including nurses) evaluates the individual’s need for hospitalization and notifies the court of their treatment recommendations. This specialized mental health care is referred to as forensic psychiatry. [27]
Discharge
When clients with mental health disorders are hospitalized, their admission status may impact their rights related to discharge. There are four main types of discharge [28] :
- Unconditional Discharge: Unconditional discharge refers to unconditional termination of the legal patient and institution relationship. Discharge may be ordered by a psychiatrist, advanced practice provider, or the court.
- Release Against Medical Advice (AMA): Clients who were admitted voluntarily may elect to leave an institution against the advice of the health care provider.
- Conditional Release: Conditional release means the client is discharged from inpatient care but requires outpatient treatment for a specified period of time. If the client was involuntarily admitted, they can be readmitted based on the original commitment order if they don’t participate in outpatient treatment.
- Assisted Outpatient Treatment: Assisted outpatient treatment means the conditional release is court-ordered. This treatment is tied to services and goods provided by social welfare agencies, such as disability benefits and housing.
Reporting Unsafe or Impaired Professionals
Patients have the right to humane treatment and reasonable protection from harm. For example, if a suicidal patient is admitted and left alone with the means of self-harm, the nurse has a duty to protect the patient and can be held liable for injuries or death that occurs.
Nurses also have a duty to protect patients from suspected negligence by a colleague. In many states, nurses have a legal duty to intervene and report risks of harm to patients. This may include reporting concerns to a supervisor, the institution, and/or the state Board of Nursing. For example, nurses must report suspected drug diversion by colleagues because it can impact safe and humane treatment of patients. Read more about drug diversion and substance use disorder in nursing in the “ Substance Use Disorders ” chapter.
View the NCSBN PDF pamphlet: A Nurse’s Guide to Substance Use Disorder in Nursing .
- Cady, R. F. (2010). A review of basic patient rights in psychiatric care. JONA'S Healthcare Law, Ethics and Regulation, 12 (4), 117–127. https://doi.org/10.1097/NHL.0b013e3181f4d357 ↵
- This work is a derivative of Nursing Fundamentals by Open RN and is licensed under CC BY 4.0 ↵
- Middleman, A. B., & Olson, K. A. (2021, August 10). Confidentiality in adolescent health care. UpToDate. Retrieved February 22, 2022, from https://www.uptodate.com/ ↵
- Cady, R. F. (2010). A review of basic patient rights in psychiatric care. JONA'S Healthcare Law, Ethics and Regulation, 12 (4), 117–127. https://doi.org/10.1097/NHL.0b013e3181f4d357 ↵
- Cady, R. F. (2010). A review of basic patient rights in psychiatric care. JONA'S Healthcare Law, Ethics and Regulation, 12 (4), 117–127. https://doi.org/10.1097/NHL.0b013e3181f4d357 ↵
- Halter, M. (2022). Varcarolis’ foundations of psychiatric-mental health nursing (9th ed.). Saunders. ↵
- Cady, R. F. (2010). A review of basic patient rights in psychiatric care. JONA'S Healthcare Law, Ethics and Regulation, 12 (4), 117–127. https://doi.org/10.1097/NHL.0b013e3181f4d357 ↵
- Halter, M. (2022). Varcarolis’ foundations of psychiatric-mental health nursing (9th ed.). Saunders. ↵
- Cady, R. F. (2010). A review of basic patient rights in psychiatric care. JONA'S Healthcare Law, Ethics and Regulation, 12 (4), 117–127. https://doi.org/10.1097/NHL.0b013e3181f4d357 ↵
- The Joint Commission. https://www.jointcommission.org/ ↵
- The Joint Commission. https://www.jointcommission.org/ ↵
- The Joint Commission. https://www.jointcommission.org ↵
- Wood County, Wisconsin. (n.d.). Guardianship and protective placements. https://www.co.wood.wi.us/Departments/HumanServices/GuardianshipAndProtectivePlacement.aspx ↵
- Knox, D. K., & Holloman, G. H., Jr. (2012). Use and avoidance of seclusion and restraint: Consensus statement of the American Association for Emergency Psychiatry Project Beta Seclusion and Restraint Workgroup. The Western Journal of Emergency Medicine 13 (1), 35-40. https://doi.org/10.5811/westjem.2011.9.6867 ↵
- Moore, G. P., & Pfaff, J. A. (2022, January 12). Assessment and emergency management of the acutely agitated or violent adult. UpToDate. Retrieved February 23, 2022, from https://www.uptodate.com/ ↵
- Moore, G. P., & Pfaff, J. A. (2022, January 12). Assessment and emergency management of the acutely agitated or violent adult. UpToDate. Retrieved February 23, 2022, from https://www.uptodate.com/ ↵
- Moore, G. P., & Pfaff, J. A. (2022, January 12). Assessment and emergency management of the acutely agitated or violent adult. UpToDate. Retrieved February 23, 2022, from https://www.uptodate.com/ ↵
- Cady, R. F. (2010). A review of basic patient rights in psychiatric care. JONA'S Healthcare Law, Ethics and Regulation, 12 (4), 117–127. https://doi.org/10.1097/NHL.0b013e3181f4d357 ↵
- Cady, R. F. (2010). A review of basic patient rights in psychiatric care. JONA'S Healthcare Law, Ethics and Regulation, 12 (4), 117–127. https://doi.org/10.1097/NHL.0b013e3181f4d357 ↵
- Cady, R. F. (2010). A review of basic patient rights in psychiatric care. JONA'S Healthcare Law, Ethics and Regulation, 12 (4), 117–127. https://doi.org/10.1097/NHL.0b013e3181f4d357 ↵
- Cady, R. F. (2010). A review of basic patient rights in psychiatric care. JONA'S Healthcare Law, Ethics and Regulation, 12 (4), 117–127. https://doi.org/10.1097/NHL.0b013e3181f4d357 ↵
- Cady, R. F. (2010). A review of basic patient rights in psychiatric care. JONA'S Healthcare Law, Ethics and Regulation, 12 (4), 117–127. https://doi.org/10.1097/NHL.0b013e3181f4d357 ↵
- Halter, M. (2022). Varcarolis’ foundations of psychiatric-mental health nursing (9th ed.). Saunders. ↵
- Cady, R. F. (2010). A review of basic patient rights in psychiatric care. JONA'S Healthcare Law, Ethics and Regulation, 12 (4), 117–127. https://doi.org/10.1097/NHL.0b013e3181f4d357 ↵
- Halter, M. (2022). Varcarolis’ foundations of psychiatric-mental health nursing (9th ed.). Saunders. ↵
- Cady, R. F. (2010). A review of basic patient rights in psychiatric care. JONA'S Healthcare Law, Ethics and Regulation, 12 (4), 117–127. https://doi.org/10.1097/NHL.0b013e3181f4d357 ↵
- Cady, R. F. (2010). A review of basic patient rights in psychiatric care. JONA'S Healthcare Law, Ethics and Regulation, 12 (4), 117–127. https://doi.org/10.1097/NHL.0b013e3181f4d357 ↵
- Halter, M. (2022). Varcarolis’ foundations of psychiatric-mental health nursing (9th ed.). Saunders. ↵


5.9: Effects of Plate Tectonics
EXPLAIN HOW ROCK FORMATIONS, GEOLOGIC ENVIRONMENTS, MINERAL RESOURCES, VOLCANOES AND THEIR ERUPTIONS, LANDFORMS, MOUNTAIN BUILDING PROCESSES, CLIMATE CHANGE, EVOLUTION, FOLDS, FAULTS AND EARTHQUAKES RELATE TO AND ARE AFFECTED BY PLATE TECTONICS
[Insert brief introductory statement here.]
Open Educational Resources
The outcome for this section will be covered by several Open Educational Resources. Review and reflect on each one as you prepare to complete the assessment for this module.
- Reading: The Ring of Fire
- Reading: Intraplate Deformation
- Reading: Folds
- Reading: Climates and Tectonics
Contributors and Attributions
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Original content from Kimberly Schulte (Columbia Basin College) and supplemented by Lumen Learning . The content on this page is copyrighted under a Creative Commons Attribution 4.0 International license.


5: Experimental Characterization - Spectroscopy and Microscopy
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- 5.1: Model Membranes vs. Biological Membranes
- Model-based studies have proven to be very useful in understanding basic biophysical properties of biological membranes. They provide a foundation upon which new hypotheses can be generated and tested in living cells. A solid foundational understanding of simple synthetic membranes should allow scientists to develop experimental and computational tools to test more complex properties of biological membranes.
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- 5.2: Supported and Tethered Membranes
- Model lipid bilayers or synthetic lipid bilayers are membranes that are created in vitro. In vivo studies of lipid bilayers and the proteins embedded within them can be difficult due to the complexity of the cellular dynamics of membranes. Model bilayers use biological membranes, along with artificial constraints, to investigate the structure and function of lipid bilayers. Supported and tethered membranes are two types of model bilayers frequently used in model studies.
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- 5.3: Styrene Maleic Acid Lipid Particles (SMALP) Technology
- Styrene maleic acid lipid particles (SMALPs) are disc-shaped lipid assemblies on the nano-scale made from the interaction of membrane bilayers and styrene maleic acid (SMA) copolymer. SMALP technology holds great potential as a biochemical tool as it allows solubilization of membrane bilayers and its embedded constituent into discs without any use of detergents. SMALPs are thought to be superior to other disc-forming techniques.
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- 5.4: Lipid Probes
- Lipid labeling offers an alternative to destructive methods and allow for measurement made in native environments without immobilization. There are three major types of lipid probes: fluorescent probes can be used for identifying target membranes or lipids, spin-probes are useful for measuring membrane dynamics, and isotopic probes are often used for membrane composition analysis.
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- 5.5: Fluorescence on Membranes
- The study of membranes poses a unique challenge in science due to their complex and fluid nature. Until recently, the majority of experiments was conducted in either fixed samples or on population levels that did not give insight into individual events. However, recent advances in fluorescence microscopy techniques have allowed scientists to visualize microscopic perturbations of individual vesicles and have allowed the study of membrane dynamics at higher spatiotemporal resolution than before.
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- 5.6: Near-field Scanning Optical Microscopy (NSOM)
- Near-field scanning optical microscopy(NSOM), also called scanning near-field optical microscopy(SNOM), is a scanning probe technique that overcomes the diffraction barrier in traditional far-field optical microscopy. Conventional optical microscopy techniques are limited by the diffraction of the light and the resolution is limited to roughly 250 nm, which make it very difficult to resolve the domains or clusters in the cellular membranes.
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- 5.7: Single Molecule Tracking
- Single Molecule Tracking (SMT), also known as Single Particle Tracking (SPT) or Single Dye Tracking (SDT), refers to a class of non-invasive techniques that involve direct spatial observation of individual molecular or particle entities as a function of time. This Wiki page offers a broad overview of the some of the working principles, technical aspects, and biophysical applications of SMT.
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- 5.8: FTIR on Membranes
- Fourier Transform Infrared (FTIR) Spectroscopy is a widespread, relatively cheap technique for studying the structure of compounds through chemical bond vibrations. Since there are already pages dedicated to FTIR and Attenuated Total Reflectance Fourier Transform Infrared Spectroscopy (ATR-FTIR) this page will not go into the details of the theory associated with these techniques, but will instead describe these techniques in relation to lipid membranes.
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- 5.9: Raman Spectroscopy on Membranes
- Biochemical compounds of interest like lipids have been studied and their corresponding Raman shifts have been characterized. Lipids are characterized as oily molecules that are soluble in non-polar solvents and are not miscible in water. Some common lipids that can be studied are Cholesterol, saturated and fatty acids, Triglycerides and Phospholipids and many more.
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- 5.10: Nuclear Magnetic Resonance (NMR) Theory and Solution NMR
- Nuclear magnetic resonance (NMR) occurs when nuclei in an unmoving magnetic field are disturbed by an oscillating magnetic field; the nuclei generate an electromagnetic signal, whose frequency depends on the magnetic field applied. This happens near resonance, where the frequency of oscillation aligns with the frequency of the nuclei. The magnetic field strength, chemical environment, and isotope affect resonance.
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- 5.12: Electron Paramagnetic Resonance (EPR) of Membranes
- Electron paramagnetic resonance (EPR) is a technique with applications in multiple branches of science, including physics, biology, and chemistry. The basic concepts of EPR are known to be analogous with Solid-state NMR, except it is electron spins that are excited as opposed to spins of atomic nuclei.
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- 5.13: Membrane X-ray Scattering
- Membrane scattering encompasses a huge variety of methods for characterizing lipid membranes. For example, a few popular techniques include X-ray or neutron reflectivity and diffraction, Brewster angle microscopy, ellipsometry, X-ray interferometry, infrared reflection-adsorption spectroscopy, and vibrational sum frequency generation spectroscopy. These methods can be used with a variety of different model membranes types.
Thumbnail: S. cerevisiae septins revealed with fluorescent microscopy utilizing fluorescent labeling. (Public Domain, Spitfire ch,).